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Solving linear equations and linear inequalities — Basic example

Video transcript
- [Voiceover] Three L minus six is greater than or equal to eight. Which of the following best describes the solutions to the inequality shown above? So it's three times L minus six is greater than or equal to eight. Well all of these choices, these are in terms of L. They've said L on one side is greater than or equal to, actually all of these choices are greater than or equal to something else. So let's see what we can do to get just an L on the left-hand side. So the first thing we might want to do is let's get rid of this subtracting the six, and the best way we can do that is we can add six. Let's add six to both sides. This six and this six are going to add to zero, and then we are going to be left with, we are going to be left with three L on the left hand side is greater than or equal to eight plus six is 14. Now to just get an L on the left-hand side we can divide both sides by three, and if you divide both sides by three, you're not going to change the sign, you're not going to change the inequality. If you're dividing by a negative number, you would swap the inequality. Greater than or equal to would turn into less than or equal to, but we're dividing by a positive number, so this is going to be L is greater than or equal to 14 over three which is that choice right there.